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ivann1987 [24]
3 years ago
15

(c) The total number of one centimeter lines in the first n diagrams is given by the expression

Mathematics
1 answer:
trapecia [35]3 years ago
4 0

Answer:

I) f + g = 10/3

II) 4f + 2g = 20/3

III) f = 2 and g = 4/3

Step-by-step explanation:

From the chart,

P = 25

q = 40

The total number of one centimeter lines in the first n diagrams is given by the expression 

2/3n^3 + fn^2 + gn. 

When n = 1, the total number of line = 4. So,

2/3(1)^3 + f(1)^2 + g(1) = 4

2/3 + f + g = 4

Make f+g the subject of formula

f + g = 4 - 2/3

f + g = (12 - 2)/3

f + g = 10/3 ......(1)

When n = 2

Total number of line = 12

2/3(2)^3 + f(2)^2 + g(2) = 12

2/3×8 + 4f + 2g = 12

16/3 + 4f + 2g = 12

4f + 2g = 12 - 16/3

4f + 2g = (36 - 16)/3

4f + 2g = 20/3 ......(2)

(iii) To find the values of f and g, solve equation 1 and 2 simultaneously

f + g = 10/3 × 2

4f + 2g = 32/3

2f + 2g = 20/3

4f + 2g = 32/3

- 2f = - 12/3

f = 12/6

f = 2

Substitutes f in equation 1

f + g = 10/3

2 + g = 10/3

g = 10/3 - 2

g = (10 - 6)/3

g = 4/3

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Which two transformations must be applied to the graph of y = ln(x) to result in the graph of y = –ln(x) + 64?
stiks02 [169]

Answer: A) reflection over the x-axis, plus a vertical translation

Step-by-step explanation:

Ok, when we have a function y = f(x)

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then for a funtion g(x), this tranformation can be written as h(x) = -g(x).

> A vertical translation of A units (A positive) up for a function g(x) can be written as: h(x) = g(x) + A.

Then in this case we have:

y = g(x) = ln(x)

and the transformed function is h(x) = -ln(x) + 64

Then we can start with h(x) = g(x)

first do a reflection over the x-axis, and now we have:

h(x) = -g(x) = -ln(x)

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3 years ago
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Step-by-step explanation:

Given the rational expression: \frac{2x + 3}{x^2 - 5x + 4}, to express this in simplified form, we would need to apply the concept of partial fraction.

Step 1: factorise the denominator

x^2 - 5x + 4

x^2 - 4x - x + 4

(x^2 - 4x) - (x + 4)

x(x - 4) - 1(x - 4)

(x- 1)(x - 4)

Thus, we now have: \frac{2x + 3}{(x- 1)(x - 4)}

Step 2: Apply the concept of Partial Fraction

Let,

\frac{2x + 3}{(x- 1)(x - 4)} = \frac{A}{x- 1} + \frac{B}{x - 4}

Multiply both sides by (x - 1)(x - 4)

\frac{2x + 3}{(x- 1)(x - 4)} * (x - 1)(x - 4) = (\frac{A}{x- 1} + \frac{B}{x - 4}) * (x - 1)(x - 4)

2x + 3 = A(x - 4) + B(x - 1)

Step 3:

Substituting x = 4 in 2x + 3 = A(x - 4) + B(x - 1)

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B = \frac{11}{3}

Substituting x = 1 in 2x + 3 = A(x - 4) + B(x - 1)

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A = -\frac{5}{3}

Step 4: Plug in the values of A and B into the original equation in step 2

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\frac{2x + 3}{(x- 1)(x - 4)} = \frac{-5}{3(x- 1)} + \frac{11}{3(x - 4)}

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3 years ago
5/7^3 = 5(7^x)<br> Thank you for helping!!
SIZIF [17.4K]

When solving this equation you get x = -3.

To solve this, simply follow the order of operations for solving.

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Since both x and -3 are the powers of x, we can eliminate the 7 and just make the exponents equal.

-3 = x

8 0
3 years ago
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